Quadratics

Algebraic Expansion

100

Expand k(7-4k)

7k-4k²

200

Expand (x-2)(x+2).

x²-4

300

Expand (x-4)(x-6)

x²-10x+24

400

Expand 2x(x²-4)+3x³-6x²+5

5x³-6x²-8x+5

500

Expand 2(m+2)(m+1)(m-3)

2m³-14m-12

Algebra: Factorisation

100

Factorise 9k-k².

k(9-k)

200

Factorise 121-m².

(11+m)(11-m)

300

Factorise 3x²+13x-10.

(3x-2)(x+5)

400

Solve for 741²-259² without using a calculator.

741²-259²

=(741+259)(741-259)

=(1000)(482)

=482000

500

If 2x²-2y²=125 and x-y=2.5, find the value of x+y.

2x²-2y²=125 

2(x²-y²)=125 

(x²-y²)=62.5

(x-y)(x+y)=62.5

2.5(x+y)=62.5

x+y=25

Quadratic Equation

100

x² + 3x – 4 = 0

What is x = –4, x = 1.

200

2x2 – 4x – 3 = 0

What is x = –0.58, x = 2.58

300

9x² + 12x + 4 = 0

x = –2/3

400

3x² + 4x + 2 = 0.

No solution.

500

Solve (x-2)²+(x+3)²=50

(x-2)²+(x+3)²=50

x²-4x+4+x²+6x+9=50

2x²+2x-37=0 (Use quadratic formula)

x = –4.83, x = 3.83

Quadratic Function

100

Find the vertex of the quadratic function y=-x²-5x+4.

Vertex is (-2.5, 10.25)

200

Write the quadratic equation in y=a(x-p)(x-q) form that has solutions of -2 and 3.

y=(x+2)(x-3)

300

Write the quadratic equation in y=ax²+bx+c form that passes through points (-2,0), (5,0), and (0,-10).

y=x²-3x-15

400

Write the quadratic function in vertex form, y=a(x-h)²+k, of the graph shown by Ms. Olive 

Note: (h,k) is the vertex.

y=-.5(x-1)²+8

500

Write a quadratic function in standard form with the following condition:

1) x-intercepts: 1 negative and 1 positive

2) y-int at (0,8)

3) concave downward

^{Show your equation to Ms. Olive.}

Real World Quadratics

100

The sum of the squares of two consecutive even integers is 340. Find the two integers.

12 and 14

200

George is 5 years older than Harry. If the product of their ages is 234., find Harry's present age.

Harry's present age is 13 years old.

300

A rectangle has dimensons (3x+1) cm by (2x+1) cm. Given that the area of teh rectangle is 117 cm². Find the perimeter of the rectangle.

The perimeter of the rectangle is 44 cm.

400

A stone is thrown vertically upwards from the top of a cliff. It's height, h metres, above the level ground, can be modelled by h=28+42t-12t², where t is the time in seconds after the stone has been thrown.

At what time will the stone strike the ground.

At 4.07 sec, the stone will strike the ground.

500

Ricky kicks a soccer ball vertically upwards. the height, h metres, of the ball can be modelled by h=27t-6t², where t is the time in seconds after it leaves the ground.

Find the maximum height of the ball above the ground and the time at which it occurs.

The ball reaches the height of 30.5 m at 2.25 sec.